Recent studies have demonstrated that muscle force is not determined solely by activation under dynamic conditions, and that length history has an important role in determining dynamic muscle force. Yet, the mechanisms for how muscle force is produced under dynamic conditions remain unclear. To explore how muscle force production is determined under dynamic conditions, we investigated the effects of muscle stiffness, activation, and length perturbations on muscle force. First, submaximal isometric contraction was established for whole soleus muscles. Next, the muscles were actively shortened at three velocities. During active shortening, we measured muscle stiffness at L₀ and the force response to time-varying activation and length perturbations. We found that muscle stiffness increased with activation but decreased as shortening velocity increased. The slope of the relationship between maximum force and activation amplitude differed significantly among shortening velocities. Also, the intercept and slope of the relationship between length perturbation amplitude and maximum force decreased with shortening velocities. As shortening velocities were related with muscle stiffness, the results suggest that length history determines muscle stiffness and the history-dependent muscle stiffness influences the contribution of activation to muscle force and the contribution of length perturbations to muscle force. A three-parameter viscoelastic model that included a linear spring and linear damper in parallel with tunable history-dependent spring stiffness proportional to measured muscle stiffness predicted history-dependent muscle force with high accuracy. The results and simulations support the hypothesis that muscle force under dynamic conditions can be accurately predicted as the force response of a history-dependent viscoelastic material to length perturbations.

Protocol 1 measured how muscles respond to time-varying activation depending on muscle stiffness. Muscles were stimulated isometrically at submaximal voltage (3.87 ± 0.88 V) and frequency (5 Hz) until they until they reached a steady-state force of 7.0 ± 3.0% P₀ in ~ 0.7s. Once isometric force reached steady state, active shortening was performed at two velocities (1.0 L₀/s, 0.5 L₀/s) and under isometric conditions. At the midpoint of active shortening, muscle length was held constant at L₀ by changing the starting length (Fig. 1, blue). To evaluate how muscle force depends on the amplitude of activation, the amplitude of activation during active shortening was varied using an A-M Systems Model 4100 stimulator (A-M Systems, Sequim, Washington, USA). 

            In protocol 1, activation started increasing at the onset of active shortening. The amplitude of activation increased linearly for 100ms, and then decreased linearly for 100ms (Fig. 1, red). Peak activation occurred at the midpoint of active shortening at muscle optimal length (L₀). Six different activation amplitudes were used: 100%, 110%, 120%, 130%, 140% and 150% of the amplitude for the first submaximal isometric contraction (see above). To measure instantaneous muscle stiffness, quick length transients (0.9% L₀ at a speed of 3L₀/s) were performed at L₀ during active shortening.

            In protocol 2, the response of muscle force to length perturbations was measured for different values of muscle stiffness, established by varying the shortening velocity. As in protocol 1, isometric contraction and active shortening at 1.0 and 0.5 L₀/s were performed (Fig. 2, blue). Length perturbations were performed at the midpoint of active shortening where muscle length was L₀ in all trials. The shape of the length perturbation was varied based on a half sinusoidal curve at a frequency of 2.5 Hz. For the trials with no active shortening, the amplitudes of the sinusoidal curve were 0.2%, 0.4%, 0.6%, 0.8%, 1%, and 3% of L­₀ (Fig. 2B, blue), and for the trials with active shortening, the amplitudes were 1%, 3%, 5%, 7%, 9% and 11% of L₀ (Fig. 2A, blue). Activation was constant at ~35% of P₀ (Fig. 2A, B, red). Instantaneous muscle stiffness was measured at L₀ using a quick length transient (0.9% L₀, 3 L₀/s).

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